### All GMAT Math Resources

## Example Questions

### Example Question #31 : Inequalities

Give the solution set of the inequality

**Possible Answers:**

**Correct answer:**

To solve a quadratic inequality, move all expressions to the left first:

The boundary points of the solution set will be the points at which:

: that is, , or

: that is, .

None of these values will be included in the solution set, since equality is not allowed by the inequality symbol.

Test the intervals

by choosing a value in each interval and testing the truth of the inequality.

: Test

True; include the interval .

: Test

False; exclude the interval .

: Test

True; include the interval .

The solution set is .

### Example Question #31 : Inequalities

Give the solution set of the inequality

**Possible Answers:**

**Correct answer:**

To solve a rational inequality, move all expressions to the left first:

The boundary points of the solution set will be the points at which:

- that is, ;

; and

- that is, .

None of these values will be included in the solution set, since equality is not allowed by the inequality symbol.

Test the intervals

by choosing a value in each interval and testing the truth of the inequality.

- test

False - exclude

- test

True - include

- test

False - exclude

- test

True - include

The solution set is .

### Example Question #131 : Algebra

Give the solution set of the inequality

**Possible Answers:**

**Correct answer:**

The square of a real number must be nonnegative, so this is a true statement regardless of the value of . The solution set is the set of all real numbers

To solve a quadratic inequality, move all expressions to the left first

The boundary points of the solution set will be the points at which:

; that is, ; or,

; that is,

These values will be included in the solution set, since equality is allowed by the inequality symbol.

Test the intervals

by choosing a value in each interval and testing the truth of the inequality.

: test

False - exclude this interval

: test

True - include this interval

: test

False - exclude this interval

is the solution set.

### Example Question #1221 : Problem Solving Questions

Solve for :

**Possible Answers:**

**Correct answer:**

can be rewritten as the inequality

(note the change in direction of the inequality symbols)

This is the set .

### Example Question #1222 : Problem Solving Questions

Solve the following inequality:

**Possible Answers:**

**Correct answer:**

Like any other equation, we solve the inequality by first grouping like terms. Grouping the terms on the left side of the equation and the constants on the right side of the equation, we have:

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